Texture UVUnwrap Follow Up-- What did I do wrong?
Figured out what I was doing wrong. I deleted my file, and started from scratch. I realized that like what @DiogoValadares said, I have to actually put the "maps" / islands on the texture while in the UV texture editor. Unwrapping it cleanly isn't enough. To do this, go to your UV editor, then in the bottom left to the right of "UVs" tab, press the little image icon and select the texture you want.